Short multiplication

What it is

Short multiplication is the written method for multiplying a number by a single digit. The number goes on top, the single digit sits underneath it in the ones column, and each digit of the top number is multiplied in turn, starting at the ones. A column that makes ten or more sends the tens of it on to the next column, which is what carrying is.

Two things have to hold for the method to work. Table facts have to arrive fast enough not to interrupt it, and the carried digit has to be added after the next multiplication rather than multiplied with it: in the tens column above, 4 × 7 = 28 comes first and the carried 1 is added to it, making 29.

This is also the first row of long multiplication, which is this method run twice and the two rows added, so it is worth being secure here before Year 5.

When children learn it

Year 4 is where the National Curriculum asks children to multiply two-digit and three-digit numbers by a one-digit number using formal written layout, and the same year expects recall of all the tables to 12 × 12. Year 3 leads into it, moving from mental methods to written ones for two-digit numbers times one-digit numbers. Year 5 keeps this method and adds a two-digit multiplier.

What it looks like when it goes wrong

These patterns come up again and again in children's answers on this skill. Each one points at a specific missing idea, not carelessness.

• Every carry dropped. 342 × 7 answered as 2184. Each column was multiplied correctly and written down whole where it fitted: 2 × 7 made 14 and the 4 was written, 4 × 7 made 28 and the 8 was written, and neither ten moved on. The answer looks tidy, so an estimate catches it faster than rereading: 342 × 7 is about 350 × 7, which is about 2450.
• Added instead of multiplied. 342 × 7 answered as 349. Short multiplication is set out like column addition, and under pressure the more familiar operation takes over. Asking what the × sign is asking for, before the pencil moves, is usually enough.
• A table fact one out. The layout is right, the carrying is right, and the answer is one away from correct, because one of the table facts inside it was one out. This is not a problem with the method: it is times tables showing through the method, and it is the tables that need the practice.

How to help at home

• Ask for an estimate before the working starts: 342 × 7 is about 350 × 7, so about 2450. That one habit catches a dropped carry without checking any of the digits.
• Check the table facts the calculation needs before doing the calculation. If 4 × 7 takes thinking time, every column is being built out of a fact that is still being worked out.
• Ask what happens to a carried digit. It is added after the next multiplication, never multiplied with it, and saying that out loud once tends to settle it.
• Use squared paper, one digit per square. A good part of what looks like an arithmetic error is a column that drifted.

Other guides

• Long multiplicationThe Year 5 method for multiplying by a two-digit number: what the second row's zero is for, and where answers go wrong.
• Times tablesHow recall builds from Year 2 to the Year 4 multiplication check, and what shaky tables look like.
• Short divisionThe bus stop method: Year 4 for divisions that come out exactly, Year 5 for remainders, and how it leans on tables.